Belgium international Vertonghen started 22 of Tottenham's league games last season but was overlooked against promoted Villa, with Davinson Sanchez and Toby Alderweireld getting the nod ahead of him.
After John McGinn's early opener gave Villa a lead they held until the 73rd minute, an equaliser from Tanguy Ndombele and a double from Harry Kane helped Spurs to victory.
Pochettino said Vertonghen's omission was purely tactical, telling Sky Sports: "With all the players fit, in the future we're going to struggle to find the starting 11. We have more than 25 that are knocking on the door of the first team.
"We have plenty of very good players in all the positions. We cannot play with 13 or 14. It's always the judgement of the manager and coaching staff. If we lose, my decisions were so bad; if we win, we keep going.
"I'm going to play the players who I believe deserve to play. There's not any issue.
"Jan for sure, like any other player who didn't play today, is going to have to work hard for the opportunity to play, and show me that I was wrong when they didn't play."
The introduction of Christian Eriksen as a second-half substitute seemed to lift Spurs nine minutes before Ndombele scored with a superb long-range strike on his debut.
Pochettino admitted his first-half game plan did not work, saying: "We were a little bit confused but it's always my fault because I'm the manager.
"Our positional game ... it didn't work in the first half, to be honest. We started to make rash decisions and found positions that didn't help us. That was my fault.
"Second half we fixed that problem. We helped the team to move the ball better.
"Adding Christian fresh helped the team to achieve the victory, but we are talking about a top-quality player."
Opposite number Dean Smith handed debuts to four of his 12 summer signings, with Tom Heaton, Bjorn Engels, Trezeguet and Wesley all featuring for the first time in competitive action for Villa.
Smith dismissed the suggestion his new signings might have struggled to gel, saying: "It's not that hard, actually.
"I've worked with five of the players before so the integration has been quite seamless. They've all adapted and now we've learned the standard of what we need. Anybody who comes here is going to find it tough against the team Mauricio has got. It's a great learning curve."
Looking ahead to his side's clash with Everton at Villa Park on August 23, their first home Premier League game since 2016, Smith added: "We always looked and thought Villa Park would be massive for us this season.
"We'll go and put in performances for the fans at Villa Park and I hope we can be a threat."